We introduce Axiom VII (Prime-Selective Actualization, PSA) as a foundational extension of the Universal Model Framework (UMF). While earlier UMF axioms, in particular the invariant information-rate principle (Axiom VI, PIR-I), constrain the kinematically admissible configuration space of physical systems, PSA addresses the unresolved question of actualization: why only a restricted subset of admissible configurations manifests as persistent physical reality. PSA postulates that physical configurations are those information patterns that remain stable under prime-indexed recursive validation, implemented via renormalization-group–like operators acting across prime scales. Configurations that fail this stability criterion remain mathematically admissible but physically unrealized. This principle provides a unified explanatory mechanism for (i) natural quantization, (ii) effective measurement selection without invoking fundamental collapse postulates, and (iii) emergent irreversibility via directional accumulation of validation. The axiom is formulated in a mathematically explicit and falsifiable manner, with direct empirical constraints derived from anomalous scaling exponents. In particular, PSA predicts universal holographic scaling with anomalous dimension η≈2\eta \approx 2η≈2; systematic deviation from this value would falsify the axiom. The framework is deliberately substrate-independent and does not posit consciousness or observers at the axiomatic level, although higher-order self-validation processes may admit cognitive or agent-like interpretations in specific realizations. Axiom VII completes the logical structure of UMF by separating what is allowed (PIR-I) from what becomes physically real, offering a testable selection principle at the foundations of physics. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
We introduce Axiom VII (Prime-Selective Actualization, PSA) as a foundational extension of the Universal Model Framework (UMF). While earlier UMF axioms, in particular the invariant information-rate principle (Axiom VI, PIR-I), constrain the kinematically admissible configuration space of physical systems, PSA addresses the unresolved question of actualization: why only a restricted subset of admissible configurations manifests as persistent physical reality. PSA postulates that physical configurations are those information patterns that remain stable under prime-indexed recursive validation, implemented via renormalization-group–like operators acting across prime scales. Configurations that fail this stability criterion remain mathematically admissible but physically unrealized. This principle provides a unified explanatory mechanism for (i) natural quantization, (ii) effective measurement selection without invoking fundamental collapse postulates, and (iii) emergent irreversibility via directional accumulation of validation. The axiom is formulated in a mathematically explicit and falsifiable manner, with direct empirical constraints derived from anomalous scaling exponents. In particular, PSA predicts universal holographic scaling with anomalous dimension η≈2\eta \approx 2η≈2; systematic deviation from this value would falsify the axiom. The framework is deliberately substrate-independent and does not posit consciousness or observers at the axiomatic level, although higher-order self-validation processes may admit cognitive or agent-like interpretations in specific realizations. Axiom VII completes the logical structure of UMF by separating what is allowed (PIR-I) from what becomes physically real, offering a testable selection principle at the foundations of physics. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
The Universal Model Framework (UMF) develops physical reality from a minimal set of distinction-logic axioms, prime-indexed renormalization structure, and information-theoretic constraints. While earlier axioms establish existence (Prime-Selective Actualization) and dynamical consistency (RG-anchored evolution), a foundational gap remained: the emergence of localized perspective, contextual measurement, and observer-relative frames within an otherwise global informational substrate. This work introduces Axiom VIII: Recursive Self-Localization (RSL), a necessary closure principle stating that only recursively self-modeling, compression-stable subsystems admit localized experiential frames. RSL is formulated mathematically via bounded information flow, Kolmogorov compression ratios, and predictive closure under validation dynamics. Without introducing new ontological primitives, the axiom derives locality, contextuality, temporal directionality, and observer multiplicity as structural consequences of recursive self-reference. RSL integrates consistently with prior UMF axioms and yields testable implications across quantum measurement, holographic scaling, and cosmology. In particular, it predicts universal holographic scaling with anomalous dimension η=2\eta = 2η=2, observed independently across multiple validation protocols. The result completes the UMF axiomatic ladder by explaining not only what exists and how it evolves, but why physical reality is necessarily experienced through localized frames rather than as a single undifferentiated whole. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
This publication presents an extended axiomatic revision of the Probability-Space Axiomatic Foundation. The original minimal logical core (K1–K4), governing realization, temporal asymmetry, and constrained selection among unrealized possibilities, is preserved verbatim and unchanged. This revision introduces an Extended Core (v2.0) consisting of three additional axioms (K5–K7) that are additive rather than revisionary. These axioms are required to support observer-dependent projection of observables, non-signaling correlation via shared collapse ancestry (entanglement), and the emergence of persistent relational deformation interpreted as effective curvature. The extended axioms do not modify the original logical foundation; instead, they constrain how realized structure is accessed, correlated, and stabilized when instantiated as a physical system. The work is structured as a strict in-place extension of the original manuscript. All original text, numbering, and logical development are preserved word-for-word. New material is inserted only where logically required, and is explicitly labeled as part of the Extended Core. No experimental claims are made. No force-based or field-first primitives are introduced. Physical quantities such as mass, energy, or spacetime curvature are not assumed at the axiomatic level. This axiomatic framework is intended to function as a constraint layer for physical theories built on Probability-Space concepts, ensuring compatibility with observer locality, non-signaling correlation, and emergent large-scale structure without altering the minimal logical basis. The framework is falsifiable in principle: any physical realization must recover standard quantum statistics and empirically tested gravitational behavior in appropriate limits. This record supersedes and extends the author’s prior Zenodo publication by providing a formally defined Extended Core (v2.0), while maintaining full continuity with the original axiomatic foundation.
The **Information Manifold Model (IMM) V3** presents a unified scientific framework where physical reality, spacetime, and cognition emerge from a single **informational manifold**. By using six foundational axioms, the model mathematically derives the **determinacy of observations**, suggesting that definite outcomes are a structural consequence of how information is projected. It posits that **Lorentzian spacetime** is not a fixed background but a stable attractor resulting from informational flow and renormalization. The research introduces a **unified variational principle** that seeks to harmonize general relativity, quantum mechanics, and thermodynamics under one informational action. Furthermore, the text predicts **testable deviations** from standard quantum statistics in specific mesoscopic systems, providing a pathway for empirical falsification. Finally, the model extends its reach into **cognitive architecture**, replacing traditional psychiatric categories with a dynamical systems approach to human behavior and perception.
In contemporary physics, fundamental structures such as space, time, matter, spin, and measurement are typically introduced as independent primitives or axiomatic ingredients. While quantum mechanics and relativistic field theories describe these structures with extraordinary precision, they do not explain why such structures exist, why they are discrete or stable, nor why reality manifests in exactly three spatial dimensions with an irreversible arrow of time. This work presents a unified informational–geometric framework—the Universal Gravito–Informational Theory (TGIU)—in which physical reality emerges from a pre-geometric informational substrate governed by two complementary gradients: informational coherence (Φ) and informational entropy (S). Their interaction is regulated by a real-valued dynamical mechanism composed of the Curvature–State Transform (CST) and the TGIU Equilibrium Force (TEF). Together, these operators generate bounded, orthogonal informational rotations whose stabilized projections give rise to geometry, matter, and observable physical laws. Within this framework, electron orbitals are reinterpreted as CST limit cycles, spin emerges as the topological orientation of these cycles, and the Pauli exclusion principle arises from phase–space saturation rather than postulated antisymmetry. Atomic stability, the absence of radiative decay in stationary states, fine structure, and the Lamb shift are shown to follow from TEF anisotropy and vacuum curvature granularity, while remaining fully consistent with quantum electrodynamics in its predictive domain. Measurement and wavefunction collapse are described as local TEF locking events, providing a deterministic but non-restorative mechanism for outcome selection without invoking fundamental randomness. Time itself is shown to emerge as monotonic CST phase accumulation, explaining both its one-dimensional nature and its irreversibility as geometric consequences of bounded informational curvature. The existence of exactly three spatial dimensions follows from a CST dimensional closure condition, identifying three dimensions as the only geometry capable of sustaining stable, non-divergent informational rotation. Importantly, TGIU does not replace quantum mechanics, general relativity, or field theory. Instead, it supplies a deeper explanatory layer that clarifies why these frameworks work, why their structures are constrained as observed, and why no physical process can reach absolute annihilation or infinite divergence. Extremes are not restored but redirected: identity is not conserved, yet nature persists through renewed coherence. This work positions TGIU as an empirically motivated, geometrically grounded extension of modern physics—one that unifies matter, time, measurement, and dimensionality under a single informational principle, while remaining compatible with established theories in their respective limits.
Foundational problems in physics—including quantum measurement, spacetime emergence, gravitational dynamics, nonlocality, the arrow of time, and the status of physical existence—are typically addressed in isolation, via model-dependent extensions or interpretive assumptions. This work proposes a different approach. We introduce a constraint-based framework, the Closure Admissibility Principle (CAP), which specifies minimal structural conditions any physical description must satisfy in order to be globally consistent. CAP is formulated in operational terms, using admissibility of states, recoverability under refinement, and stability of closed records, without assuming spacetime, dynamics, or ontology a priori. We show that enforcing these constraints induces a unifying closure structure on law-space, from which several persistent foundational puzzles are resolved as structural consequences rather than postulates. In particular, collapse is reclassified as record selection, spacetime and gravity emerge only in compressible regimes, General Relativity appears as an infrared universality class rather than a fundamental law, singularities correspond to failures of admissible description, and null (“nothing”) models are excluded as inadmissible fixed points. The framework is explicitly falsifiable via operational and weak-field tests, and its scope and limits are stated precisely. The results suggest that many foundational paradoxes arise not from incomplete dynamics, but from admitting globally incoherent physical descriptions.
This paper introduces Axiom 0, a minimal foundational principle for physical reality: the impossibility of any globally closed description of the total correlational structure. Rather than postulating space, time, dynamics, locality, or physical laws as primitive, the framework assumes only: (i) the existence of a correlational structure, (ii) the structural impossibility of complete self-closure, and (iii) consistency under partial comparison. From these ingredients, the paper shows how: physical laws emerge as stabilizing regularities of incomplete descriptions, time, dynamics, and geometry arise as effective, regime-dependent structures, irreversibility follows from projection and information loss, and why no description can be both exact and globally complete. Non-closure is treated as an ontological constraint, not as epistemic ignorance or observer dependence. Physical reality exists precisely because complete closure is impossible, independently of observation or modeling. The paper does not attempt to replace existing physical theories or derive numerical constants. Instead, it provides a structural foundation within which effective physical theories (quantum, classical, relativistic, and open-system regimes) can be consistently understood as emergent and domain-limited. This work is intended as a conceptual and structural foundation for correlational and relational approaches to fundamental physics, clarifying the origin of laws, dynamics, and physical regularity without invoking additional ontological postulates.